Let X be a complex space of dimension n, not necessarily reduced, whose cohomology groups H1(X,𝒪),...,Hn-1(X,𝒪) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1-convex) if, and only if, X is holomorphically spreadable (resp., X is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for 1-convexity.